Question

Holiday Inn Hotel Conducted a study of its business travelers who take trips of five nights or more. They found that 47% of these individuals rate sightseeing as their most enjoyable activity. A sample of 120 business travelers who take trips of five nights or more is selected. Let ? be a random variable for the number of travelers out of the 120 sampled who rate sightseeing as their most enjoyable activity. (a) Name the probability distribution for ?. Identify any parameter values. (b) Name a probability distribution, different from the answer in (a), that can be used to approximate the probability distribution for ?, and justify your answer. (c) Identify any parameter values associated with the distribution specified in (b). (d) Use the distribution specified in (b) to approximate the probability that more than 40 travelers in the sample of 120 rate sightseeing as their most enjoyable activity.

Answer 1

(a)

Here X has binomial distribution with parameters as follow:

n =120, p = 0.47

(b)

Since np = 56.4 and n(1-p) = 63.6 both are greater than 5 so we can use normal approximation here.

That is X will have approximately normal distribution.

(c)

Using normal approximation, X has approximately normal distribution with mean and SD as follows:

(d)

Here we need to use continuity correction factor. The z-score for X = 40 +0.5 = 40.5 is

The probability that more than 40 travelers in the sample of 120 rate sightseeing as their most enjoyable activity is